The effect of a singular term in a quadratic quasi-linear problem

2016 ◽  
Vol 19 (1) ◽  
pp. 815-831 ◽  
Author(s):  
David Arcoya ◽  
Lourdes Moreno-Mérida
Keyword(s):  
Linear Problem ◽  
Singular Term

scholarly journals A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian

2021 ◽  
Author(s):  
Yunru Bai ◽  
Nikolaos S. Papageorgiou ◽  
Shengda Zeng
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Singular Term ◽  
Type Theorem ◽  
Solution Map ◽  
Continuity Properties ◽  
Variational Tools ◽  
Superlinear Reaction

AbstractWe consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the (p, q)-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tools combined with suitable truncations and comparison techniques. We prove a bifurcation-type theorem describing in a precise way the dependence of the set of positive solutions on the parameter $$\lambda $$ λ . Moreover, we produce minimal positive solutions and determine the monotonicity and continuity properties of the minimal positive solution map.

scholarly journals Cooperative Operation Schedules of Energy Storage System and Demand Response Resources Considering Urban Railway Load Characteristic under a Time-of-Use Tariff

2021 ◽  
Vol 16 (3) ◽  
pp. 1273-1284
Author(s):  
Hye Ji Kim ◽  
Hosung Jung ◽  
Young Jun Ko ◽  
Eun Su Chae ◽  
Hyo Jin Kim ◽  
...  
Keyword(s):  
Energy Storage ◽  
Demand Response ◽  
Air Conditioning ◽  
Linear Problem ◽  
Storage System ◽  
Energy Charge ◽  
Energy Storage System ◽  
Peak Reduction ◽  
Railway Stations ◽  
Charging And Discharging Processes

AbstractThis paper proposes an algorithm for the cooperative operation of air conditioning facilities and the energy storage system (ESS) in railway stations to minimize electricity. Unlike traditional load patterns, load patterns of an urban railway station can peak where energy charge rates are not high. Due to this possibility, if applying the traditional peak-reduction algorithm to railway loads, energy changes can increase, resulting in higher electricity bills. Therefore, it is required to develop a new method for minimizing the sum of capacity charges and energy charges, which is a non-linear problem. To get a feasible solution for this problem, we suggest an algorithm that optimizes the facility operation through two optimizations (primary and secondary). This method is applied to the air-quality change model for operating air conditioning facilities as demand-response (DR) resources in railway stations. This algorithm makes it possible to estimate operable DR capacity every hour, rather than calculating the capacity of DR resources conservatively in advance. Finally, we perform a simulation for the application of the proposed method to the operation of DR resources and ESS together. The simulation shows that electricity bills become lowered, and the number of charging and discharging processes of ESS is also reduced.

A Contingency Perspective on Effective Prototyping

1993 ◽  
Vol 8 (2) ◽  
pp. 99-109
Author(s):  
Oscar Gutierrez
Keyword(s):  
Project Management ◽  
Problem Solving ◽  
Organizational Support ◽  
Linear Problem ◽  
Systems Development ◽  
Social Mechanism ◽  
Contingency Perspective ◽  
Future Developments ◽  
Product And Process ◽  
Selection Of

Current demands on prototyping emphasize increasingly complex and dynamic applications that require sophisticated social mechanism and process enablers. However, much of the emphasis placed today in systems development under prototyping focuses on the supporting technology. The imbalance between product and process perspectives under this approach is explored. A view of prototyping effectiveness is presented in terms of non-linear problem solving, adequate technical and procedural solutions, and organizational support. Implications of this view are presented on the selection of prototyping techniques and on project management concerns. Future developments in prototyping practice are explored.

scholarly journals Instability, nonexistence, and uniqueness in elasticity with porous dissipation

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
M. C. Leseduarte ◽  
R. Quintanilla
Keyword(s):  
Nonlinear Problem ◽  
Exponential Growth ◽  
Linear Problem ◽  
Linear Equations ◽  
Uniqueness Of Solutions ◽  
Time Problem ◽  
Nonexistence Of Solutions

This paper is devoted to the study of the elasticity with porous dissipation. In the context of the nonlinear problem, we prove instability and nonexistence of solutions. In the context of the linear problem, we obtain exponential growth. We also obtain uniqueness of solutions of the backward in time problem of the linear equations.

scholarly journals Remarks on Impure Quotation

2003 ◽  
Vol 17 ◽  
pp. 129-151 ◽  
Author(s):  
Mario Gómez-Torrente
Keyword(s):  
Singular Term ◽  
Simple Rule ◽  
Exact Nature ◽  
Truth Conditional

Quotation marks are ambiguous, although the conventional rules that govern their different uses are similar in that they contain quantifications over quotable expressions. Pure uses are governed by a simple rule: by enclosing any expression within quotation marks one gets a singular term, the quotation, that stands for the enclosed expression. Impure uses are far less simple. In a series of uses the quotation marks conventionally indicate that (part of) the enclosed expression is a contextually appropriate version of expressions uttered by some relevant agent. When the quotation marks have this meaning, it is tempting to think of them as contributing that indication to the truth-conditional content of the utterance. I adopt a cautious attitude towards this hypothesis, for the evidence in its favor is inconclusive. In other uses the quotation marks conventionally indicate that the enclosed expression should be used not “plainly” but in some broadly speaking “distanced” way, or that it is being so used by the utterer, and typically context makes clear the exact nature of the “distance” at stake. In these cases the quotation marks do not even appear to contribute that indication to the truth-conditional content of the utterance.

scholarly journals Existence of Solutions for the -Laplacian Problem with Singular Term

2010 ◽  
Vol 2010 (1) ◽  
pp. 584843
Author(s):  
Fu Yongqiang ◽  
Yu Mei
Keyword(s):  
Existence Of Solutions ◽  
Singular Term

Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

Effective Properties of Superconducting and Superfluid Composites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3063-3073 ◽  
Author(s):  
Leonid Berlyand
Keyword(s):  
Mathematical Model ◽  
Linear Problem ◽  
Effective Properties ◽  
Point Of View ◽  
Periodicity Cell ◽  
Unit Size ◽  
Composite Media ◽  
Homogenization Procedure

We consider a mathematical model which describes an ideal superfluid with a large number of thin insulating rods and an ideal superconductor reinforced by such rods. We suggest a homogenization procedure for calculating effective properties of both composite media. From the numerical point of view the procedure amounts to solving a linear problem in a periodicity cell of unit size.

Asymptotic analysis of some two-dimensional diffusion problems

1995 ◽  
Vol 448 (1933) ◽  
pp. 213-236 ◽  
Keyword(s):  
Linear Problem ◽  
Vacancy Concentration ◽  
Surface Concentration ◽  
Two Dimensional ◽  
Surface Source ◽  
Dimensional Diffusion ◽  
Equilibrium Vacancy ◽  
Equilibrium Vacancy Concentration ◽  
Dimensional Surface ◽  
Diffusion Problems

In this paper we discuss two-dimensional surface source and implant problems for a substitutional-interstitial diffusion model. We present asymptotic solutions in the limit of the surface concentration of impurity (or peak concentration of the implant) being far greater than the equilibrium vacancy concentration. Using leading order composite solutions we plot contours of constant impurity concentration. Some of these contours differ markedly from those of the corresponding linear problem, having the ‘bird’s beak’ shape which is frequently observed in experiments. We also discuss a two-dimensional surface source problem for a va­cancy model.

Cauchy problems involving a Hadamard-type fractional derivative

2018 ◽  
Vol 68 (6) ◽  
pp. 1353-1366
Author(s):  
Rafał Kamocki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Unique Solution ◽  
Nonlinear Problem ◽  
Point Theorem ◽  
Linear Problem ◽  
Cauchy Formula ◽  
Cauchy Problems

Abstract In this paper, we investigate some Cauchy problems involving a left-sided Hadamard-type fractional derivative. A theorem on the existence of a unique solution to a nonlinear problem is proved. The main result is obtained using a fixed point theorem due to Banach, as well as the Bielecki norm. A Cauchy formula for the solution of the linear problem is derived.

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